A new DOA-based factor graph geolocation technique for detection of unknown radio wave emitter position using the first-order Taylor series approximation

Abstract

This paper proposes a new geolocation technique to improve the accuracy of the position estimate of a single unknown (anonymous) radio wave emitter. We consider a factor graph (FG)-based geolocation technique, where the input are the samples of direction-of-arrival (DOA) measurement results sent from the sensors. It is shown that the accuracy of the DOA-based FG geolocation algorithm can be improved by introducing approximated expressions for the mean and variance of the tangent and cotangent functions based on the first-order Taylor series (TS) at the tangent factor nodes of the FG. This paper also derives a closed-form expression of the Cramer-Rao lower bound (CRLB) for DOA-based geolocation, where the number of samples is taken into account. The proposed technique does not require high computational complexity because only mean and variance are to be exchanged between the nodes in the FG. It is shown that the position estimation accuracy with the proposed technique outperforms the conventional DOA-based least square (LS) technique and that the achieved root mean square error (RMSE) is very close to the theoretical CRLB.

AOA-Based Three-Dimensional Positioning and Tracking Using the Factor Graph Technique

“…Interestingly, considering both φ and θ with 3D detection, the RMSEs in 2D are found smaller than the case where only φ is used, which are closer to the theoretical CRB bound. This finding proves the fact that the information carried by the elevation angle θ also contributes to the detection in the 2D plane, which was ignored in the previous works [16]. Therefore, the introduction of the elevation angle is not only for realizing 3D detection, but also for enhancing the entire system performance.…”

“…The outputs of (A φ , A θ ), i.e., (m φ , σ 2 φ ) and (m θ , σ 2 θ ), are then sent to the factor nodes (T A , T B , T C ) for trigonometric calculations, which triggers the FG iterations. As shown in Figure 2, T A only takes the information from A φ and then feeds its outputs to the variable nodes ∆x and ∆y, which forms a completed 2D location detection as in [16]. The calculations within the factor node T A are referred to (3) and (5).…”

“…In this section, the proposed ACRB for the DOA-based 3D location detector is derived. Based on the result in [16], the conventional CRB is given by:…”

“…The performance was shown to achieve the maximum likelihood (ML) bound with relatively low complexity. Due to such advantages, many extensions of the FG algorithm to other applications can be found in [14][15][16] for received-signal-strength (RSS), TDOA, and AOA, respectively. This work will also focus on FG for both location detection and tracking.…”

“…Therefore, this paper will focus on AOA. In [16,18,19], AOA-based location detection and tracking was studied. However, the previous works only considered the scenarios in 2D.…”